This novel is the life story of an ordinary, middle-aged woman – Stella. Only that she is not ordinary because Tessa Hadley is writing her into existence and is behind her like a following wind. Perhaps the oddest thing about this odd, accomplished, elegant novel is its title, Clever Girl. It strikes a false, disassociated note. Who is speaking? Hadley herself? A passing headmistress? Or is this, as so often happens nowadays, a title wished on the book by its publishers?

Stella is a clever girl though – and Hadley cleverer still. She makes one believe every word of Stella's story. But to feel engaged, to need to read on, you want to feel Stella could be a friend. I believed in her but could not warm to her. Other readers may fare better. For me, the book was a random encounter accelerating into unwelcome intimacy. One of the things that makes Stella hard to like is that, although we become intimate with the details of her life, she seems always to be partly unavailable as a character or withheld.

There are compensations. Hadley writes as a masterly illustrator might draw. Take the buttons Stella finds on a London bomb site: "… a coral rose, wooden toggles, a diamante buckle, big yellow bone squares, toggles made of bamboo…" or the moustache of milk above a careless lip or the semi-rural dereliction of the local stables. Wherever the narrative finds itself, Hadley's eye for detail is penetrating. And having been born at roughly the same time as Stella, I can vouchsafe that her evocation of the decades is breathtakingly good. She conjures an atmosphere in less time than it takes to set a table. Take this dining room: "chilly and transitional: papered olive-green, with doors at either end and a serving hatch, African violets on the windowsill, a memory of stale gravy in the air".

Stella has two sons by different fathers and brings them up in Bristol, in the house of a homosexual English master. An idea that literature is in competition with life persists. "Men or books? With relief, I chose books." But don't believe it. Stella fetches up with Mac, a comfortable older man, whose diverse domestic talents include making "special bolognese sauce with chicken livers". Intermittently, she broods about how to inhabit time – and there is a sense that Hadley half wishes she could depart from fiction into philosophy.

It is a novel full of confident assertions. Stella describes falling in love: "Because he wasn't my type, I had fallen for him too fast and too deep, with no markers to signal any way back." She reflects: "The substantial outward things that happened to people were more mysterious than all the invisible turmoil of the inner life." Or: "That's all tyranny is: it's not in personality, it's in a set of circumstances." About each of these fluent pronouncements one is at first seduced but then, almost immediately afterwards, doubtful.

Whatever the reservations, Hadley pleasantly surprises by surrounding Stella with nice characters where a less assured novelist would have opted for villains. Stella's stepfather not only sports velvety black eyebrows, he is "energetic, intelligent, diligent, faithful…" and of the man she thinks might be her father – a driving instructor – she says: "I liked him, in spite of his dated lazy cowboy style." People don't have to be rotters because of where they show up in a story.

As the narrative hurtles on, the crucial things often happen in brackets – flash-forwards. Nicky, father of Stella's second son, is introduced with barely time to register his existence before he has died. And no sooner have we sighed with vicarious contentment at Stella's reunion with Mac than she is briskly announcing: "Of course, I regretted it marrying Mac Beresford." Then they are getting on like a house on fire again. It is confusing, but like life.

At one point, Stella reflects that books tend to be about lives derailed – another fragile generalisation. I would love to have been able to stop her own story in its tracks, to have influenced the journey of this peculiar, readable yet aimless novel, to have been able to ask: tell me a bit more about her? Or: whatever happened to him? And: did being clever matter in the end?

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